The present invention relates to a method and an apparatus for measuring the speed of sound of a gas. The speed of sound of a gas is particularly useful for determining other gas characteristics.
Accurate measurements of the speed of sound of a gas may be made using a resonator as disclosed in an article entitled Spherical Acoustic Resonators by M. Bretz, M. L. Shapiro and M. R. Moldover in volume 57 of the American Journal of Physics. The resonator containing a sample of a test gas has an acoustic transmitter and an acoustic receiver mounted in its wall. The acoustic transmitter is driven over a range of frequencies and the amplitude of the signal provided by the acoustic receiver is detected for each frequency at which the acoustic transmitter is driven. The frequency at which the acoustic receiver picks up the strongest, sharpest signal ie the first resonant radial mode is detected. Since the resonating frequency is a linear function of the speed of sound of the test gas in the resonator, the speed of sound of the test gas may be determined.
For a spherical resonator of given radius, the enclosed gas will exhibit a series of acoustic resonances. The resonances are the result of three dimensional standing waves. For a perfect system the resonant frequencies (f) are a function of the root of a spherical Bessel function (z), the speed of sound (c) and the radius of the sphere (r) given by:
f=cz/(2xcfx80r)
The radial mode is used because in this mode sound impinges on the wall of the sphere at right angles and so does not suffer energy loss due to viscous drag and so produces a sharp resonant peak which is not difficult to detect accurately.
Previous researches using a basic mathematical model of acoustic spherical resonators have reported an accuracy of 0.02% in speed of sound measurements.
However, since the resonant frequency of the spherical resonator is inversely proportional to the radius of the sphere, the resonator normally has a diameter of at least 12 cm to produce a first resonant radial mode within the frequency range of the acoustic transducers. However, a resonator of this size is too large to be used in a probe to be inserted conveniently into a source of gas such as a gas pipe or for use in a convenient and compact housing. If the resonator were to be reduced to a sphere of diameter 3 cm for example the first resonant radial mode would occur at about 18 kHz which would be beyond the range of acoustic transducers (20 Hz-13 kHz).
According to a first aspect of the present invention an apparatus for determining the speed of sound of a gas comprises:
a substantially spherical resonator for containing gas to be tested;
an acoustic transmitter for applying an acoustic signal to the interior of the resonator;
an acoustic receiver for detecting the amplitude of the acoustic signal in the interior of the resonator; and
control means for determining the speed of sound of a test gas from the frequency of a detected resonant mode;
wherein the detected resonant mode is a non-radial resonant mode and the internal radius of the resonator is substantially 5 cm or less.
According to a further aspect of the present invention a method of determining the speed of sound of a gas comprises:
applying an acoustic signal to the interior of a substantially spherical resonator containing a gas the speed of sound of which is to be determined;
detecting the amplitude of the acoustic signal in the interior of the resonator; and
determining the speed of sound of the gas within the resonator from the frequency of a detected resonant mode;
wherein the detected resonant mode is a non-radial resonant mode and the internal radius of the resonator is substantially 5 cm or less.
The inventor uses a first non-radial resonance which occurs at a frequency below that of the previously used first resonant radial mode. This first non-radial mode can be used to detect the speed of sound with resonators of smaller size than previously whilst still maintaining the resonant frequency within the range of the transducers. Consequently a more compact resonator may be used as a probe for example and may be inserted into existing gas pipes or installed into a more compact housing for greater convenience whilst still producing accurate results.
The resonator may have an internal radius of substantially 4 cm or less, 3 cm or less, 2 cm or less or preferably substantially 1.5 cm or less to make it conveniently compact.
For a substantially spherical resonator with a radius of 1.5 cm it has been found that the first non-radial mode occurs in a gas at around 9 kHz which is well within the frequency range of acoustic transducers (20 Hz-13 kHz).
The use of spherical resonators gives the most accurate speed of sound measurements. Because the sphere is symmetrical in all planes through its centre, corrections due to thermal expansion etc can be relatively easily applied.
Additionally, the acoustic transmitter and receiver can be positioned outside the resonator cavity and hence do not significantly perturb the resonating system. In contrast, using a cylinder, the acoustic transmitter and receiver affect the path length and any expansion in the transmitter and receiver must be allowed for as well as the expansion of the cylinder.
It has been found that the relative linear position of the acoustic transmitter and receiver is critical in achieving a sharp resonance curve for the first non radial resonant mode to provide accurate resonant frequency and hence speed of sound measurements. It has been found that this relative position may be slightly different for each resonator due to constructional variations. To allow for this the acoustic transmitter and receiver are preferably mountable to the resonator such that their relative separation is variable. Their relative positions can then be varied during calibrating to achieve optimum peak sharpness.
For the first non-radial mode, when the resonator is substantially spherically shaped, the acoustic transmitter and receiver are preferably positioned substantially opposite each other ie substantially 180xc2x0 apart for the largest amplitude detected peak.
Previously acoustic transmitters have operated at high voltages, eg 150 V for the transmitter in the article by M. Bretz et al mentioned above. However, this can be potentially hazardous if the resonator is working with a highly combustible gas eg methane or natural gas. The smaller resonator of the present invention may be used with a miniature, low voltage, eg 5 volt transmitter as may be used as a hearing aid speaker for greater safety.